Propagation of Errors Workshop

PRINT 1st  STUDENT NAME:                                                    PRINT 2nd  STUDENT NAME:

Suppose you collected the following data for constructive interferrence in the Michelson experiment:

({{W, 2.2, 2.3, 2.1, 1.9, 1.8}})

1. Calculate the average \(TraditionalForm\`W\&_\) and standard deviation σ  for the above data. Your "best estimate" for W is \(TraditionalForm\`W\&_\).  The uncertainty in W (or dW) is σ.  Express your numerical result in the standard form

\(W\&_\)± σ

2.  The accuracy of the measurement is 0.1 cm or 1 mm since this is the smallest measurement on the "ruler".  However, σ is different from 0.1 cm.  Why is σ the uncertainty in this measurement (and not 0.1 cm)?

3.  The wavelength λ=2W in this experiment.  Calculate the best value of the wavelength.  How is the best value of λ related to the best value of W?

4.  The uncertainty in wavelength is dλ.  Since λ is a function of W we may write λ=λ[W].  This function is especially simple for this problem and is λ=2W.  Using calculus we may write

dλ = d(λ/dW) dW

Using λ=2W show how dλ is related to dW=σ in this problem.

5.  Using the formula for dλ from problem 4 and dW=σ from problem 1, give the best value of λ and the uncertainty dλ in numerical form.  Express your answer in standard form

λ±dλ